An Alternating Iterative Method and Its Application in Statistical Inference  

作　　者：Ning Zhong SHI Guo Rong HU Qing CUI 

机构地区：[1]Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics, Northeast No~nal University, Changchun 130024, P. R. China [2]Department of Basic Courses, Shijiazhuang Railway Institute, Shijiazhuang 050043, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2008年第5期843-856,共14页数学学报（英文版）

基　　金：the National Natural Science Foundation of China (Nos.10431010,10501005);Science Foundation for Young Teachers of NENU (No.20070103)

摘　　要：This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems, the objective functions are not convex. In this paper, we give a definition of a semi-convex objective function and discuss the corresponding non-convex programming problems. A two-step iterative algorithm called the alternating iterative method is proposed for finding solutions for such problems. The method is illustrated by three examples in constrained estimation problems given in Sasabuchi et al. （Biometrika, 72, 465472 （1983））, Shi N. Z. （J. Multivariate Anal., 50, 282-293 （1994）） and El Barmi H. and Dykstra R. （Ann. Statist., 26, 1878 1893 （1998））.This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems, the objective functions are not convex. In this paper, we give a definition of a semi-convex objective function and discuss the corresponding non-convex programming problems. A two-step iterative algorithm called the alternating iterative method is proposed for finding solutions for such problems. The method is illustrated by three examples in constrained estimation problems given in Sasabuchi et al. （Biometrika, 72, 465472 （1983））, Shi N. Z. （J. Multivariate Anal., 50, 282-293 （1994）） and El Barmi H. and Dykstra R. （Ann. Statist., 26, 1878 1893 （1998））.

关 键 词：semi-convex function alternating iterative method accumulation point maximum likelihood estimation order restriction 

分 类 号：O174.13[理学—数学]